Both bikes you have considered are good for a beginner rider. The Honda CB350 H'ness will feel like a more spacious and larger machine than the Hunter, which will be a good thing if you are a larger rider. 

On the flip side, with its smaller size and 17-inch wheels, the Royal Enfield Hunter 350 will feel more agile and flickable in city traffic. Do bear in mind that coming from an Activa, both these bikes will feel quite heavy, weighing 181kg.

Something that will be similar to a ride but substantially lighter will be the TVS Ronin, which weighs 160kg. We recommend you take a look at the Ronin instead of the two 350s. Even though you are familiar with how to operate a clutch and change gears in a car, on a motorcycle, it is a different ballgame. 

Do take a test ride of the machines you shortlist before you decide. 

Since you are dissatisfied with TVS' aftersales experience, we would recommend you take a look at scooters from Japanese brands. 

Options like the Suzuki Access, Honda Activa 110 / 125 and Yamaha RayZR / Fascino Hybrid models have cemented their reputation for reliability, easy spare parts availability (especially so for the Activa and Access) and low running costs. 

These scooters are also comfortable, practical and quite fuel efficient, so picking between them will boil down to which one you prefer personally. A test ride of all these should help you make a decision. 

Since you have had a bad experience with TVS recently, we'll recommend you take a look at the Suzuki Access, Honda Activa 110 / 125 models and the Yamaha Fascino / RayZR Hybrid. These Japanese scooters have an excellent reputation for reliability and are generally uncomplicated and inexpensive to service. 

We must mention that the current TVS Jupiter 110 / 125 are some of the most well-rounded scooters in our opinion, and should you be willing to look past your bad experience, these should serve you well. 

A test ride of all these options, as well as a chat with the service manager for these scooters. It will help paint a clearer picture and help you make an informed decision. 

Unfortunately, within your budget, you won't find a brand-new machine from a reputed Japanese or European maker on the market today. In fact, some of the most affordable big bikes in India, like the Kawasaki 650s, Triumph Trident 660 and the Honda CB750 Hornet, all start above the Rs 7 lakh (ex-showroom) mark, with GST 2.0 partly contributing to this.

If you are open to the idea of a used machine, you will find Kawasaki Z650 / Ninja 650 and perhaps even a Honda CBR650F in your budget. Do bear in mind that you need to be cautious and do a thorough background check on these machines. Because a replacement mechanical part will cost you a pretty penny. And these older bikes also won't be E20 petrol compatible, so that's another factor to consider.